| Titre : | Extropy of Ordered Variates |
| Auteurs : | Ibtissem Aissaoui, Auteur ; Nour Elhouda Zouaoui, Directeur de thèse |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2024 |
| Format : | 1 vol. (47 p.) / couv. ill. en coul / 30cm |
| Langues: | Anglais |
| Résumé : |
Shannon entropy, established by Shannon in 1948 and widely utilized in reliability and information studies, has seen a recent counterpart in extropy, proposed by Lad et al. (2015), which serves as its dual measure. This master’s thesis aims to present the concept of extropy, a measure of uncertainty. One statistical application of extropy is to score the forecasting distributions. It addresses the problem of extropy of ordered variates records and order statistics and related properties. Simplified expressions of the extropy of ordered variates are derived. |
| Sommaire : |
Contents Dedication i Acknowledgment ii Abstract iii Notations and symbols iv Table of Contents vii List of figures ix List of tables x Introduction 1 1 Records and Order Statistics 3 1.1 Order Statistic . . . . . . . . . 3 1.1.1 Ordinary Order Statistics . . . . . . . .. . 4 1.1.2 K-Order Probability Density Function . . . .. 5 1.2 Record Statistics . . . . . . . . . . . . . . . . . . . 8 1.2.1 Ordinary Record Statistics . . . . . . . . . . 8 1.2.2 Record Probability Density Function . . . . . 9 1.2.3 k-Record Statistics . . . . . . . . . . . . 11 2 Extropy of Records and Order Statistics 20 2.1 Background . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Preliminaries . . . . . . . . . . . . . . . . . 22 2.3 Extropy of Record Statistics . . . . . . . . . . .. . 24 2.3.1 The Extropy of nth Value of k-Records . . . . . . . . . . . 24 2.3.2 Some Results and characterizations based on record statistics 27 2.4 Extropy of order Statistics . . . . . . . . . 30 2.4.1 The Extropy of mth order statis . . . 30 2.4.2 Some Results and characterizations based on order statistics 31 2.5 Some numerical computation . . . . . . . . . . . . . . . . . . . . . 33 2.5.1 Upper and Lower record values . . . . . . . .. . 33 2.5.2 Extropy of upper record . . . . . . . . 36 2.5.3 Extropy of the first order statistic . . . . . 39 Conclusion 40 Bibliography 42 Annexe A: Logiciel R 46 2.6 What is the R language? . . . . . . . 46 2.7 R code used at chapter 2 . . . . 47 viii |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| MM/1274 | Mémoire master | bibliothèque sciences exactes | Consultable |
